This section is intended to introduce various aspects of the art, which may be associated with exemplary embodiments of the present techniques. This discussion is believed to assist in providing a framework to facilitate a better understanding of particular aspects of the present techniques. Accordingly, it should be understood that this section should be read in this light, and not necessarily as admissions of prior art.
As hydrocarbon reservoirs that are easily harvested, such as oil reservoirs on land or reservoirs located in shallow ocean water, are used up, other hydrocarbon sources must be used to keep up with energy demands. Such reservoirs may include any number of unconventional hydrocarbon sources, such as biomass, deep-water oil reservoirs, and natural gas from other sources.
One such unconventional hydrocarbon source is natural gas produced from shale, termed “shale gas.” Because shale may have insufficient permeability to allow significant fluid flow to a well bore, many shales are currently not considered as commercial sources of natural gas. However, shale gas has been produced for years from shales with natural fractures. Recently, a significant increase in shale gas production has resulted from hydraulic fracturing, which is used to create extensive artificial fractures around well bores. When combined with horizontal drilling, which is often used with shale gas wells, the hydraulic fracturing may allow formerly unpractical shale layers to be commercially viable.
Shales that host economic quantities of gas have a number of common properties. They are rich in organic material and are usually mature petroleum source rocks in the thermogenic gas window. They are often sufficiently brittle and rigid enough to maintain open fractures, over a short period. Some of the gas produced is held in natural fractures, some in pore spaces, and some is adsorbed onto the organic material. The gas in the fractures can be produced immediately, while the gas adsorbed onto organic materials may be released as the formation pressure declines.
The fracturing process is complicated and can be modeled to improve the efficiency of the fracturing. A more efficient fracturing process may lead to a more productive reservoir. In other words, a greater amount of the gas trapped in a shale layer may be harvested. As discussed below, a number of researchers have proposed different techniques for modeling the growth of fractures in various rock formations.
In Perkins, T. K., and Kern, L. R., “Widths of Hydraulic Fractures,” JPT, September, 222 Trans. AIME 937-949 (1961), a fluid mechanics study was performed on the rupture of brittle materials and the theory of elastic deformation of rock. The results indicated that for a given formation, crack (or fracture) width is essentially controlled by fluid pressure drop. High pressure drops result in relatively wide cracks, while low pressure drops result in relatively narrow cracks.
In Rice, J. R. and Rosengren, G. F., “Plane strain deformation near a crack tip in a power-law hardening material,” 16 J. Mech. Phys. Solids 1-12 (1968), crack-tip strain singularities were investigated with the aid of an energy line integral exhibiting path independence for all contours surrounding a crack tip in a two-dimensional deformation field. Elastic and elastic/plastic materials were studied. The study determined that the product of stress and strain exhibits a singularity varying inversely with distance from the tip in all materials.
In Nordgren, R. P., “A Propagation of a Vertical Hydraulic Fracture,” SPEJ, August, 306-314, Trans., AIME, 253 (1972), the propagation of hydraulic fractures of limited vertical and elliptic cross-section were studied with the inclusion of fluid loss. The study determined that the fracture length and width grow faster with time in the no-loss than in the large loss case.
In Leung, C. K. Y., and Li, V. C., 24 Journal of Materials Science 854-862 (1989), an experimental technique for indirectly determining a tension-softening curve, was developed. The tension-softening curve is suggested to be a size-independent fracture ‘parameter’ for quasi-brittle materials. The technique was based on generating specimens that had a large size and a four-point bending mode.
In McDowell D. L., Miller M. P., and Brooks D. C., “A Unified Creep-Plasticity Theory for Solder Alloys”, 42 Fatigue Electronic Material AST STP 1153 (1994), the fracture behavior of solders was investigated. The goals of the study were to develop a thermo-mechanical unified creep-plasticity model, which could be used to characterize the response of solders, and to characterize a selected solder alloy through mechanical testing and correlation with the model across a range of strain rates, temperatures, aging times, and loading-unloading conditions. The model allowed the performance of solders under fatigue and creep-plasticity interactions due to thermo-mechanical cycling to be modeled.
In Benzeggagh and Kenane, “Measurement of mixed-mode delamination fracture toughness of unidirectional glass/epoxy composites with mixed-mode bending apparatus,” 56 Composites Sci. Tech. 439-449 (1996), the initiation of cracking and delamination growth in a unidirectional glass/epoxy composite were evaluated under mode I, mode II, and mixed mode I+II static loading. In addition to the characterization of delamination, the apparatus allowed the plotting of an R curve, from which a total fracture resistance, GTR, could be obtained.
In Martin, A. N., “Crack Tip Plasticity: A Different Approach to Modelling Fracture Propagation in Soft Formations,” SPE 63171 (2000), a crack tip plasticity (CTP) method was developed, which assumed a fracture tip of finite radius, with a zone of plastically deformed material around it. The plastic zone forms when stresses on the rock increase beyond the yield point of the rock, at which point the rock starts to flow plastically. The plastic zone acts to absorb extra energy from the fracturing fluid, making it harder to propagate fractures through formations with significant plastic deformation. This in turn means that, for a given ductile material, fractures will be smaller and less conductive than those predicted by LEFM.
In van Dam, D. B., “Impact of Rock Plasticity on Hydraulic Fracture Propagation and Closure,” SPE 63172 (2000), scaled laboratory experiments of hydraulic fracture propagation and closure in soft artificial rock and outcrop rock samples were performed. Numerical simulations of the fracture behavior in plastic rocks were also performed, using independently measured rock properties. The simulations aided in interpreting the measurements and extrapolating the results to field scale. Plasticity induces a larger width in a fracture for a given net pressure, compared with elastic rock. However, the pressure to propagate fractures was only marginally increased and, in the case of laboratory tests, was actually lower than expected from elastic behavior. The most dramatic effect of plasticity is that closure is much lower than the confining stress due to strong stress redistribution along the fracture.
In Dean, R. H. and Schmidt, J. H., “Hydraulic Fracture Predictions with a Fully Coupled Geomechanical Reservoir Simulator,” SPE 116470 (2008), a geomechanical reservoir simulator was developed that combined hydraulic fracture growth, multiphase/multicomponent Darcy/nonDarcy porous flow, heat convection and conduction, solids deposition, and poroelastic/poroplastic deformation in a single application. The program contained two separate criteria that could be used to model fracture propagation: a critical fracture-opening criterion based on a stress intensity factor and a cohesive zone model that used quadrilateral cohesive elements in the fracture. The cohesive zone model includes a cohesive strength and an energy release rate in the calculations at the tip of a propagating hydraulic fracture.
U.S. Patent Application Publication No. 2008/0091396 by Kennon, et al., provides a method and system for modeling and predicting hydraulic fracture performance in hydrocarbon reservoirs. An unstructured automatic mesh is generated and computational algorithms are executed using a finite element numerical approach. The method is to model a hydrocarbon reservoir, wells, and completions as a single system, accounting for static information and transient behavior of wells, hydraulic fractures, and reservoirs in a single model. Models used for the fracture behavior are not disclosed.
Most of the current hydraulic fracture modeling in the oil industry continues to rely on empirical models, or on numerical methods based on linear elastic fracture mechanics (LEFM). Generally, these methods are valid for brittle materials and give reasonable predictions for hydraulic fractures in hard rocks. However, for ductile rock, such as shale, clay, weakly consolidated sandstones (low cohesion granular materials), or other relatively less brittle, softer, and/or more deformable rocks, the LEFM-based methods typically give overly conservative and often limited-use or unuseful predictions of fracture geometry.